Walk. The historic centre is compact — less than 2 km from the station to Piazzale Michelangelo — and most of it is pedestrianised or restricted. Walking from the Accademia to the Uffizi to Palazzo Pitti takes about 25 minutes.
The orange ATAF buses (€1.70 a journey, €5 for 90 minutes) serve the wider city and the hills. Line 13 goes to Piazzale Michelangelo. The T1 and T2 trams connect the airport, the station, and the western suburbs.
Taxis are metered and expensive from ranks. Ride-hailing is limited. For Fiesole and the surrounding countryside, the bus services are good and cheap. Cycling is popular in the city; bike-share schemes operate with docking stations across the centre.
Do not try to drive or park in the ZTL (the pedestrianised centre) unless you have accommodation in it — the automatic cameras issue fines of €80–130 to foreign plates, often arriving at home months later.